Pistachio yield prediction using multiple linear regression and artificial neural network (A Case Study: Rafsanjan and Anar regions, Kerman Province)

Introduction In recent decades, due to a significant increase of pistachio cultivation and uncontrolled exploitation of groundwater resources as well as reducing rainfall precipitation, groundwater level has dropped and the quantity and the quality of water has also been reduced. Therefore, agricultural producers, researchers and policy makers need to pay more attention to appropriate land management as an important strategy to achieve greater yield per unit area and optimal use of soil and water resources. Crop yield prediction regarding its temporal and spatial variations has an important role in developing proper management programs. However, few studies have been carried out in relation to pistachio yield prediction using an acceptable range of features on regional scale. In the present study, pistachio yield modeling was performed by multivariate linear regression and artificial neural networkbased on soil, water and management features.
Materials and Methods 129 orchard plots in different areas of Rafsanjan and Anar were identified and selected. The study area is located between 54° 56′ and 56° 41′ E, 29° 54′ and 31° 13′ N. Soil sampling, was performed from the areas under pistachio canopy and three soil depths of 0 to 40, 40 to 80 and 80 to 120 cm in each plot, fully expanded sub-terminal leaflets were randomly collected from non-fruiting branches, during the late July through August. Irrigation water of all orchards was also sampled. Moreover, for each orchard, a questionnaire was prepared to collect management and yield data. Soil quality indicators including particle size distribution, pH in saturated soil paste, electrical conductivity of saturated extract, soluble sodium, soluble calcium, soluble magnesium, available phosphorus and available potassium were determined for soil samples. The concentrations of phosphorus, potassium, iron, zinc, copper, manganese, calcium and magnesium in leaf samples and electrical conductivity in water samples, were also calculated. Finally, a dependent variable (pistachio yield) and 50 independent variables including soil, water and plant characteristics were used for modeling. For this purpose, stepwise multiple linear regression and artificial neural network technique were applied. Then, the study area was divided into 4 parts with the highest pistachio orchards densities and regression models were run for each part, separately. The ability of models to yield prediction was evaluated using the root mean square error (RMSE), relative root mean square error (% RMSE), adjusted coefficient of determination (adj - R2) and Durbin - Watson statistic (D – W).
Results and Discussion The average of yield in the study area is about 1,700 kilograms per hectare. Results indicated that multiple linear regression could explain only 26 percent of the pistachio yield variation, but its accuracy increased when data became more homogeneous via dividing the study area into four parts. The model adjusted-R2 for Noogh, Anar, eastern suburbs and western suburbs orchards rose to about 92.4, 81.5, 95 and 53.6 percent, respectively. In all regression models except the model of western suburbs, at least one of the characteristics associated with irrigation water was significant. Artificial neural network with 9 neurons in a hidden layer, Tangent - sigmoid activation function and Levenberg - Marquardt training function, has a 98.3 percent accuracy in predicting pistachio yield in the study area (% RMSE = 13.8).
Conclusion Multivariate linear regression model did not accurately predict the pistachio yield for the whole of study area whereas increasing data homogeneity and decreasing sources of variations, reduced complexity of relationships between features which resulted in increasing of the efficiency of linear regression to modeling these relationships. These models were highly sensitive to irrigation water features. Therefore, special attention should be paid to modern irrigation techniques and proper management approaches in order to enhance water efficiency. Overall, artificial neural network had greater accuracy compared to multivariate linear regression for pistachio yield modeling. This indicates the existence of non-linear and complex relationships between pistachio yield and the factors affecting yield and also the necessity of using modern and robust data mining tools for crop yield estimating. It seems that artificial intelligence techniques can be used as an efficient tool for developing proper management programs.